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Un Calcul De Constructions Infinies Et Son Application A La Verification De Systemes Communicants
, 1996
"... m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to ..."
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m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to Luc Boug'e, who accepted to be my oficial supervisor, and to the chair of the jury, Michel Cosnard, who opened to me the doors of the LIP. During these last three years in Lyon I met many wonderful people, who then become wonderful friends. Miguel, Nuria, Veronique, Patricia, Philippe, Pia, Rodrigo, Salvador, Sophie : : : with you I have shared the happiness and sadness of everyday life, those little things which make us to remember someone forever. I also would like to thank the people from "Tango de Soie", for all those funny nights at the Caf'e Moulin Joly. Thanks too to the Uruguayan research community in Computer Science (specially to Cristina Cornes and Alberto Pardo) w
Domain theoretic formulation of linear boundary value problems
 Proc. CiE 2005, number 3526
, 2005
"... Abstract. We present a domain theoretic framework for obtaining exact solutions of linear boundary value problems. Based on the domain of compact real intervals, we show how to approximate both a fundamental system and a particular solution up to an arbitrary degree of accuracy. The boundary conditi ..."
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Abstract. We present a domain theoretic framework for obtaining exact solutions of linear boundary value problems. Based on the domain of compact real intervals, we show how to approximate both a fundamental system and a particular solution up to an arbitrary degree of accuracy. The boundary conditions are then satisfied by solving a system of imprecisely given linear equations at every step of the approximation. By restricting the construction to effective bases of the involved domains, we not only obtain results on the computability of boundary value problems, but also directly implementable algorithms, based on proper data types, that approximate solutions up to an arbitrary degree of accuracy. As these data types are based on rational numbers, no numerical errors are incurred in the computation process. 1
A Proposal for Reasoning in Agents: Restricted
"... Abstract. JohnsonLaird proposes a semantic theory of human reasoning taking into account finite human capacities. We cast this into logical formalism and define a notion of restricted semantic entailment. Corresponding to any set of logical structures, R, there is a restricted entailment with param ..."
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Abstract. JohnsonLaird proposes a semantic theory of human reasoning taking into account finite human capacities. We cast this into logical formalism and define a notion of restricted semantic entailment. Corresponding to any set of logical structures, R, there is a restricted entailment with parameter R. The family of restricted entailments, generated as R varies over sets of structures, is shown to be a complete lattice and to approximate ordinary entailment in the sense of domain theory. A given restricted entailment, �R say, can be modelled in a modal language with an operator ↓R. The modal language is sound and complete and there is a correspondence result: X �R ϕ iff ↓RX ⊩↓Rϕ, where X is a set of firstorder sentences and ϕ is firstorder. This forms the basis for the proposal that �R be identified with agent reasoning and that ↓R encapsulate an agent. The existence of the lattice structure mentioned above means that several agents can be integrated into a superagent or else distilled into a subagent by taking joins or meets. 1